Prof

by Dermot Turing

  The precaution which the Poles were exploiting was based in the need for a German sender to let his recipient know what ‘message setting’ he was using. It was all very well for the recipient to have a chart showing which wheels were going to be used, and which ring-settings, and what cross-pluggings, for any given day, but to add further complexity the starting positions of the coding wheels in their slots were to be different for each message. The procedure was for the sender to pick a starting position at random, and to let his opposite number know which three letters he was using by transmitting them at the beginning of the transmission. It would be too obvious, and too helpful to enemy intelligence, to transmit the three starting-position letters ‘in clear’, so the sender enciphered them. And here was the precaution: Morse code is easily garbled, and without any verbal context there was a danger that the starting position would be incorrectly received and the message would decrypt as gobbledegook, and have to be re-sent. Re-sending messages is very bad security (Bletchley’s biggest breakthroughs came when messages were re-sent), so the precaution against garbling was to transmit the enciphered starting position twice. Of course, on a small scale, this was making the re-sending error, and the Germans discontinued the practice in 1940. Indeed, the Allies knew they would, sooner or later, do so. But in the meantime, the Poles had used the duplicated transmission to identify which wheels were being used and their relative positions, using giveaways known to the British codebreakers as ‘females’. Females happened when the same letter appeared in both versions of the enciphered triplet in the same place – for example, if CIL was transmitted as ABN MRN.

  Here was the germ of an idea which let the Poles in and from which the machine designed by Alan Turing grew. The same letter (L in this example, but what it actually was was unknown to eavesdroppers) had somehow got encrypted as N with the coding wheels in, for example, positions 3 and 6. If two Enigma machines were rigged up together, but three positions out of phase, they could test one by one all 17,576 combinations to find one – in fact there would be many – which allowed a letter to be enciphered as N at positions 3 and 6. If there were other females on the same net on the same day, the number of potentially correct combinations could be reduced. And if the relative positions of the coding wheels were found, the Poles were already a long way towards knowing the complete Enigma settings of the day.

  The Poles explained the principles behind their bomba machine to Dilly Knox in Poland in July 1939, a mere five weeks before the invasion. The simultaneous testing of different enciphered letters at staggered positions in the message was a general principle, even if the Poles had applied it to the special case of ‘females’. Yet the principle could be exploited further by the British, to test an intercepted message against guessed-at plain-text (a ‘crib’). If replica Enigma machines were wired up together into a loop, the configuration of coding wheels in the German Enigma machine would be open to identification.

  That left the problem of the plugboard. Alan Turing’s idea was to apply electric voltage to one wire only in the input to the 26-wire cables connecting the replica Enigmas together. Say, for example, that voltage was applied to the wire leading to terminal ‘K’ on the first wheel of the first replica Enigma in the loop: that would identify which letter the ‘K’ was cross-plugged to, as well as finding the wheel configuration. The clever part of the idea, which might have amused Wittgenstein, was that it depended so heavily on negative information. Here was a form of halting problem given tangible mechanical form. Alan Turing designed the machine to stop when it had a plausibly good m-configuration; it knew when to do so because only in the (rare) case of a good wheel configuration, the voltage would be confined to a single wire in all cables joining the replica Enigmas. If the wheel configuration was bad, one or other of the wheels would be out of alignment, and electricity would reach other wires in the cables. In cases where all 26 wires were live, the machine was to keep on and try the next configuration of the three coding wheels.

  The machine would have to be fast, to get through 17,576 possible combinations without taking hundreds of years, and it would have to be designed to stop whenever it found a plausible combination. These were formidable engineering challenges, but the British Tabulating Machine company (an ancestor of the computer company Fujitsu) had a brilliant Chief Engineer called Doc Keen. Keen knew he could build a machine which would rattle through all 17,576 wheel positions in no time (about 12 minutes). He could also deal with the more difficult electrical challenge of having the machine stop – so the operator could read out the plausible combination of settings – whenever only one wire in the input cable was live, but carry on to test the next combination whenever all 26 wires were live. Keen and Turing understood each other – or rather, Turing understood Keen easily, and Keen was clever enough to fathom out what Turing wanted – and a prototype machine was designed, turned into blueprints, and built. In homage to the Poles, whose country was now ground under the combined heels of the Nazis and the Soviets, they called their invention the ‘Bombe’.

  While the Bombe was being assembled, the codebreakers would have to make do with manual methods. One of the Polish techniques, exploiting the double-encipherment of message settings, used cardboard sheets (called ‘Netz’ at Bletchley) with alphabets across the top and down the sides, representing all the possible positions of the right-hand and middle coding wheels. One sheet was needed for each possible combination of wheels, making, with five possible wheels to choose from, 60 sheets in all. Small holes were cut into the sheets at each point where the right-hand and middle wheels could create a ‘female’. The sheets would be piled on top of each other so that the codebreakers could see whether any holes went right through the stack, and where that happened they could identify the wheels and ring-settings in use. Creating the sheets initially involved cutting out the holes by hand with a razor blade; it was going to take 100 British codebreakers working eight hours a day about 100 years to produce them. Later they were able to punch the holes mechanically, and eventually they were able to share the workload with the French, who were working with the escaped Polish cryptanalysts outside Paris. Alan Turing was sent over in January 1940 with a set of sheets, and had the opportunity to discuss Enigma-breaking with Marian Rejewski as well as the French team. It seems that they didn’t discuss his ideas for a Bombe.

  Not a computer. The Bombe, designed by Alan Turing and Gordon Welchman, found logically plausible Enigma settings which were worth testing further.

  In February 1940 Dilly Knox’s research group broke the traffic enciphered on the ‘blue’ Luftwaffe Enigma key-net, causing Dilly to burst out into a Carrollian parody.

  ’Twas HUTSIX, and the WRANGLERCOVES

  Did twist and twiddle at the CYC;

  All grimset were the JEFFREYBROWS,

  And the BABBAGE outschreik.

  ‘Beware the SEVENTHWHEEL, my son,

  The pale FULLHOUSE, the NETZ that fail;

  Move not the UMKEHRWALZE, and shun

  The UNCONFIRMED FEMALE.’

  He took the COTTAGECROWD in hand,

  Oft times the REGISTRATORS sought;

  Then ’midst his CILLIS, SLUGS and SNAKES,

  He sat awhile in thought.

  And as they over FOSSSHEETS groan,

  A REDHOTTIP (with wheels to name)

  Came TURING through the telephone.

  And DILLIED as it came!

  4, 5 and 2! No more ado –

  The RINGSTELLUNG. Turn wheels about.

  Still doubt appal, but STECKER fall

  Uncontradicted out.

  ‘And has thou truly BROKE the BLUE?

  Come to the STORE, my BOMBE-ISH boy!

  Fetch JOSH, KITS, BOLS, AARD, CERA, WALTZ.’

  He LUFTGAUED in his joy.

  ’Twas HUTSIX, and the WRANGLERCOVES

  Did twist and twiddle at the CYC;

  All grimset were the JEFFREYBROWS,

  And the BABBAGE outschreik.

  The Bombe prototyp
e was delivered to Bletchley Park on 18 March 1940. They called it Victory. There was just one problem. Victory wasn’t going to win the war, because it couldn’t break Enigma. Still, there were other problems for Alan to work on. In particular there was the challenge of naval Enigma. Unlike the land war for Britain and France, the war at sea had begun in 1939. Convoying had begun immediately, but so had U-boat activity. On 14 October, U-47 crept into Scapa Flow and sank HMS Royal Oak. Other sinkings and minelayings indicated where the first front of the war had been established. Secondly, the German Navy used Enigma differently. Instead of enciphering the starting positions for the coding wheels on their Enigma machines and transmitting the three letters for decipherment, the Navy used a different procedure. It was evident that the Germans were using some scheme for enciphering the starting positions, but what was it?

  According to the Cryptographic History of Work on the German Naval Enigma:

  When the war started probably only two people thought that the Naval Enigma could be broken – Birch, the Head of German Naval Section and Turing, one of the leading Cambridge mathematicians who joined G.C. & C.S. for the duration of the war. Birch thought it could be broken because it had to be broken and Turing thought it could be broken because it would be so interesting to break it. Whether or not these reasons were logically satisfactory they imbued those who held them with a determination that the problem should be solved and it is to the pertinacity and force that, in utterly different ways, both of them showed that success was ultimately due. Turing first got interested in the problem for the quite typical reason that ‘no one else was doing anything about it and I could have it to myself’. He started where the Poles left off and set to work to discover how the indicating system worked using the information provided by the 100 or so messages in the period 1–8 May 1937, whose starting positions were known.

  Alan Turing needed somewhere to work, and he was established in a loft in the Stableyard. ‘He did not want coffee breaks or social meals in the mansion so Claire Harding and Elizabeth Grainger1 rigged up a pulley to send up coffee and sandwiches to him in a basket.’ Fortified by the sandwiches and coffee, Alan observed that the naval Enigma messages used two groups of four letters to encode the three coding wheels’ starting positions. He also observed that some repeated two-letter combinations suggested that each starting position was represented by a pair of letters in the eight-letter indicator; if this theory was right, two of the eight letters were padding and the other six were bigrams representing the three starting positions. He built up this theory to unpick the German naval indicator method. Not only that, but on the same night he devised a technique which would allow the whole key to be broken. But to make his technique work, the Allies would need to get hold of a bigram table from the German fleet.

  On land, 1 May 1940 was the date on which the Germans dropped double-encipherment of indicator settings and made the Polish decipherment technique obsolete overnight. France was invaded and overrun in a lightning war which shocked and terrified the British. The Battle of Britain began and an invasion of the last opponent of Nazism seemed imminent. In November 1940 a German bomber let loose a stick of bombs on Elmers School, a property adjacent to Bletchley Park which had been commandeered to house GC&CS’s traffic analysts. One landed next to Hut 4, where the German Naval Section was housed. Fortunately it failed to explode.

  Crown Inn, Shenley Brook End, Bletchley, Bucks.

  My dear Mother,

  Have just been back to Cambridge for a week’s holiday. I tried to arrange a holiday with Champ, but he was booked to go with an economist friend. So I went to Camb. & did some work. Actually Champ turned up there for last week-end. […] Came back to find great excitement as bombs had dropped 100x away the day after I went. Nobody hurt but old Mr and Mrs Roberts, whom you may perhaps remember, have left their home for time being as ceilings down, and are staying here. […] I think I shall have to go up to Rossall some time this term to talk to Headmaster about Bob’s future. […]

  Yours

  Alan

  Alan was also working on a book. In fact, Alan Turing wrote not a single published book in the whole of his career. But in the first year of the war he wrote a 150-page introduction to Enigma, and techniques for breaking it, as a training manual for new recruits. This covered not only Enigma, but also naval bigrams, manual techniques invented by Dilly and much more. It became known as ‘Prof’s book’. Alan Turing was not a professor – of the 21 men of the professor type named in Denniston’s September 1939 letters to the Foreign Office, only nine were actually professors, and indeed Alan would never become a professor – but he had acquired a nickname, and he would be ‘Prof’ to his Bletchley colleagues and friends from that time.

  Prof’s book, Page 1.

  Prof’s book also explained the thinking behind his Bombe. In actual fact, Victory was working perfectly, but the problem was that it was producing ‘stops’ far too often, giving too many suggested wheel configurations/ cross-pluggings to be checked: with this performance, it couldn’t find the settings so as to produce decrypts within a reasonable time frame. To reduce the number of ‘stops’ required a really good guessed-at plain-text crib, which would enable several – ideally at least three – loops of replica Enigmas to be wired together. And this was very hard to do at the beginning of the war, when there was only limited Enigma traffic to work with and few breaks from which to build a library of cribs. But Alan Turing was not the only brilliant mind at Bletchley Park, and another mathematician from Cambridge called Gordon Welchman had an insight of great power as well as simplicity, which would allow loops to be created from the feeblest cribs. His idea was to add a cross-wiring arrangement called the ‘diagonal board’ (which, as built, was neither diagonal nor a board, but we shouldn’t be pedantic). When added to Turing’s basic Bombe design, the diagonal board led to fewer, better stops. Now they had a machine which really worked, and after May 1940 they had much more material to work with. A second Bombe, called Agnus Dei, arrived on 8 August 1940, and from thenceforth the sins of the world could be taken away by means of decrypting Army and Air Force Enigma. It was just as well, for in August 1940 the British were fighting alone.

  Professor type meets man of God

  In fear of invasion, Alan Turing embarked on one of his famously eccentric escapades. As recounted by Alan’s brother John, by now a junior infantry officer who had just escaped from the German tanks in northern France:

  He invested in some silver ingots just in case there should be a German occupation. He took these to a remote country place pushing them along in an ancient perambulator. Having buried them there he drew a map so that he could find them after the war. The war having ended he enlisted the help of his friend Donald Michie1 to find this hidden treasure, using for the purpose a home-made metal detector. For once Alan’s science had let him down for the heavy ingots were well on their way to Australia.

  It wasn’t just the silver ingots. For many years, banned from discussing the technicalities of work at Bletchley Park, all people could recount was the oddities of their co-workers. Odd they were – the civilians, at any rate – and Alan Turing seems to have topped the bill. Many anecdotes seem to have involved his bicycle:

  • ‘He used to cycle to and from work and in the summer he would wear his civilian gas mask to ward off hayfever. This apparition caused consternation to others on the road. Some would search the skies for enemy aircraft and others would don their gas masks just to be on the safe side.’

  • ‘In the shelter during air-raids he knitted himself a pair of gloves, with no pattern to guide him, just out of his head; he was, however, defeated when it came to completion of the fingers, so he used to bicycle in from Shenley with little tails of wool dangling from his fingertips until one of the girls in his office took pity on him and closed up the ends.’

  • ‘Every now and then the chain fell off the bicycle. A normal person would then take the machine to the garage and get it mended but for him this wo
uld be the absolute last resort; a man ought to be able to confront the universe with his own bare hands and what God put inside his skull so he began to think about it. The first thing he knew was to count how many times the pedals went round and the results of counting suggested a periodicity which he thought could be due to this being a rare event which occurred whenever a particular defective cog on the larger cog wheel was in register with a defective cog on the smaller cog wheel and he investigated and he was proved right, but this was the way he went about everything.’ ‘Instead of having it mended he would count the number of times the pedals went round and would get off the bicycle in time to adjust the chain by hand.’

  Among the young recruits at Bletchley Park in 1940, the Prof was, at 28, an old boy, old enough for his oddities not to matter much. If Dilly Knox, Frank Birch, Alastair Denniston and the other veterans from the first war were the old guard, the new war had grown its own generation of leaders. By virtue of his early arrival date and his reputation, not to mention his great age, Alan Turing was becoming one of them. By 1941 he had become head of Hut 8, responsible for naval decryption.

  The occupation of northern and western France by the Germans had opened the whole of the North Atlantic to the U-boats. Now based at Lorient, they were playing havoc with the convoys. Sinkings during the period up to May 1940 averaged 113,000 tons a month; after the fall of France the monthly toll doubled. By the end of 1941 over 5 million tons – 1,124 ships – had gone to the bottom. Fighting the Battle of the Atlantic was Bletchley Park’s most urgent, but also its most difficult, challenge. But even the Bombes weren’t quite enough to enable Bletchley Park to get on top of naval Enigma. The German Navy used eight coding wheels for their Enigma machine, as contrasted with five in the other armed forces. This, in theory, meant that 336 wheel combinations had to be tested to find the machine settings, rather than 60, requiring 80 hours of Bombe time to break a setting, as compared to 14 hours for air force keys. It was time to call upon a man of God.